The present invention relates to xcex2-titanium alloy wire which is suitable for metallic wires, such as various kinds of precision springs, various kinds of ropes or cables, tension member for communication cable, probe card pin for inspection of conduction, metallic fishing line and the like. The present invention also relates to a method for producing said xcex2-titanium alloy wire and medical instruments made by said xcex2-titanium alloy wire.
Titanium is hexagonal close-packed structure (hcp, xcex1-structure) at a room temperature. Titanium is converted into body-centered cubic structure (bcc, xcex2-structure) by allotropic transformation at a temperature of 1158 K or more. A density of titanium is about 60% of that of Fe. Titanium""s specific strength (proof stress divided by density) is the maximum of all metals. Young""s modulus and thermal expansion coefficient of titanium are about a half of stainless steel""s value respectively. A specific heat, an electrical conductivity and a thermal conductivity of titanium are much lower than those values of aluminum alloy or magnesium alloy respectively. Titanium has a perfect corrosion-proofness under the oxidation environment. Titanium is corrosion-resistant to chlorine ion. As described above in detail, titanium has many good properties. Accordingly, titanium is widely utilized for heat-conducting pipes of heat exchanger of fossil power station or nuclear power station in which sea water is used for cooling, sea water desalination apparatus, various electrodes for electrolysis, petroleum refining plant and the like.
The equilibrium phase diagrams of two elements containing mainly titanium are classified into xcex1-stabilized type, xcex2-stabilized type, xcex2-eutectoid type, and xcex1-xcex2 homogeneous solid solution type. Titanium alloy is obtained by combination of xcex1-stabilized elements which raise xcex1-xcex2 transformation point by extending a xcex1-phase region to a high temperature part, xcex2-stabilized elements which lower xcex1-xcex2transformation point by extending xcex2-phase region to a lower temperature part and neutral elements which have no effects on phase-stabilization. For example, there are aluminum and tin as xcex1-stabilized elements, vanadium and chromium as xcex2-stabilized elements, zirconium and hafnium as neutral elements. Titanium alloys are classified into xcex1-titanium alloy (hcp), xcex1+xcex2type titanium alloy (hcp+bcc), xcex2-titanium alloy (bcc) according to crystal structure of phase constituting micro structure under a normal temperature.
xcex1-titanium alloy is a single phase alloy obtained by solid solution hardening as a result of addition of xcex1-stabilized elements to titanium. Aluminum, which has a large solubility limit to titanium and a high solid solution hardening capacity, is mainly used as the addition element. So, xcex1-titanium alloy is a good oxidation-resistant under a high temperature but a little poor in workability. xcex1+xcex2type titanium alloy is two phase alloy under coexistence of xcex1-phase and xcex2-phase at a normal temperature by addition of xcex1-stabilized elements and xcex2-stabilized elements. Titanium-6aluminum-4vanadium, which is a representative xcex1+xcex2type titanium alloy, has a high specific strength and a high ductility, but shows a brittleness if working conditions would not be enough controlled at hot working.
On the other hand, xcex2-titanium alloy is a single phase alloy obtained by retaining at a normal temperature xcex2-phase which have been formed under a high tempearture. xcex2-titanium alloy is good in cold workability and has a high strength and a good ductility due to heat treatment. Recently a research on xcex2-titanium alloy has been actively conducted. For example, in case of titanium-15 vanadium-3 chromium-3 tin-3 aluminum, when the conditions of cold rolling and solid solution treatment have been optimized, it is reported that a tensile strength of nearly 1900N/mm2 and an elongation of 10% have been obtained. Patent unexamined publication No. 11-71621 discloses an invention on a method for producing xcex2-phase titanium alloy bar wire which states that it is possible to improve the strength and the ductility by forming woking texture of xcex2-phase prior to aging treatment and controlling xcex1-phase transformation texture precipitated by aging treatment. The details of this invention is as follows:
xcex2-phase titanium alloy bar wire is subjected to solution treatment or hot rolling at a temperature of more than transformation temperature, followed by cold working of reduction ratio of area of 30% or more and then annealing at a range between a temperature of 100xc2x0 C. lower than xcex2-transformation point and a temperature of 10xc2x0 C. lower than xcex2-transformation point. After that, xcex2-phase titanium alloy bar wire is shaped into a fixed form and subjected to an aging treatment, resulting in obtaining a high strength and a high ductility. This invention is hereinafter referred to as the prior method for producing xcex2-titanium alloy bar wire.
Recently, it has been increasing to perform a diagnosis or a therapy by inserting a catheter into a blood vessel or a digestive tract. As to medical instruments which make use of the catheter, there are a guide wire and a catheter which is manipulated through the inside of the catheter or a stent which is placed in the aim portion after passing through the inside of catheter.
The explanation of guide wire for medical treatment will be given below. The guide wire for medical treatment is used as a guide for introducing the catheter to perform a minimally invasive treatment. Generally, the guide wire for medical treatment is pushed out from the tip of the catheter and inserted into the blood vessel. For the reason, it is necessary for the guide wire for medical treatment to pass through a serpentine blood vessel or a stenosis portion (crossability) and selectively go into a requested direction at a junction (selectivity or pushability). Also, it is preferable that the tip of the guide wire for medical treatment would be a little bent to insert into the catheter and then slightly twisted at the base of wire to select the direction toward which said tip should go by rotating the bent portion of the tip. To give a little bend is referred to as re-shaping. Accordingly, the guide wire for medical treatment should have the function that the tip would move correspondingly to the twist motion of the base (torque transmittability).
The guide wire for medical treatment may be roughly divided into two categories. One is such that its center core would be a stainless steel wire and a stainless steel coil would be wound around the distal portion of the stainless steel wire. The other is such that its center core would be a super-elastic alloy and a synthetic resin would cover the center core.
But stainless steel has a high yield strength and a good pushability. Furthermore, stainless steel is easy to make plastic deformation. As a result, when stainless steel is used as center core, it is supposed that the center core would injure the blood vessel wall at its serpentine portion or its stenosis portion. Furthermore, when the palstic deformed guide wire is pulled out, it is feared that the guide wire would injure the blood vessel wall. In addition, it is a large matter that the guide wire made of stainless steel has a very low transmittability of twisting in the serpentine blood vessel and a poor selectivity or operationality at a junction.
On the other hand, the guide wire made of super-elastic alloy has a high torque transmittability in the serpentine blood vessel but it is impossible to make re-shaping at the tip thereof. And the guide wire made of super-elastic alloy has little resistance to bending at a bend portion. For solving the above problems, the guide wire comprising the following features has been demanded. The guide wire should be easily and safely manipulated by a person in attendance on the operation. For the reason, the gudie wire needs to have a high elastic modulus, a moderate yield strength and a re-shaping characteristic.
Patent unexamined publication No.6-63151 discloses the guide wire whose center core comprising: Coxe2x80x94Nixe2x80x94Crxe2x80x94Fe alloy is coated with plastic resin as new material for center core. However, any alloy disclosed in this publication has an elastic modulus of 20000 kgf/mm2 or more. Such alloy is more unbending than stainless steel and difficult to make plastic deformation. As a result, it is possible that the alloy would injure the blood vessel wall or extends the serpentine blood vessel when it is inserted into the serpentine blood vessel.
Zirconium-amorphous alloy is disclosed in Patent unexamined publication No.11-276597 or No. 2000-297. Cu-shape memory alloy is disclosed in Patent unexamined publication No. 2000-14792. These alloys are still under the research stage and have various problems to be solved for the practical material.
Furthermore, U.S. Pat. No. 5,169,597 discloses a transplant piece made of titanium alloy having a low elastic modulus. Expensive niobium and zirconium are essential elements for this transplant piece. In case of utilizing this piece for a center core of guide wire which is machined to a thickness of 0.5 mm or less, the strength of this piece is not enough to be conducted a straight shaping under addition of tension or a tapered shaping at a tip. Accordingly, this transplant piece is not suitable for a continuous tapered shaping, a continuous straight shaping or resin coating. When center core material is manufactured by hot working using this transplant piece, there will appear the following defects. Crystal grain will become coarse and exhibit a low strength. It is difficult to obtain a smooth surface and a roundness due to oxidation of the surface during the hot working. As a result, it is necessary to be worked several times for obtaining the mechanical properties and the shape to meet the needs for the center core of guide wire.
In the catheter, it is needed that the catheter would pass through the serpentine blood vessel or the stenosis portion (pushability or crossability) by providing the catheter with a rigidity by means of introducing the wire into the rumen of the catheter and laying the wire under the catheter wall. Stainless steel wire has been used as the wire for the catheter until now. As a result, the wire for catheter has the same problems as the guide wire for medical treatment.
Stainless steel or nickel-titanium alloy has been used as placement instruments, such as stent, which is placed on the extending portion of the stenosis portion of blood vessel. As to the stent made of stainless steel, there are one which can be obtained by making a stainless steel wire zigzag and another one which can be obtained by providing a stainless steel pipe with various types of openings. However, the prior stent has not satisfied a flexibility for passing through blood vessel and a moderate rigidity after placement to suppress re-stenosis.
The problems to be solved by the present invention are broadly classified into four groups.
(1) First Problem
In accordance with the prior method for producing xcex2-titanium alloy bar wire, xcex2-phase working texture is formed by cold working of reduction ratio of area of 30% or more. Then as a result of annealing at a range between a temperature of 100xc2x0 C. lower than xcex2-transformation point and a temperature of 10xc2x0 C. lower than xcex2-transformation point, a randomization of working texture has not arisen with control of recrystallization and the work-hardened bar wire will become soft. Furthermore, since xcex2-phase titanium alloy bar wire is shaped into a fixed form and subjected to an aging treatment, it is possible to precipitate fine xcex1-phase in xcex2-phase and improve the strength.
As described above, in accordance with the prior method for producing xcex2-titanium alloy bar wire, it is possible to heighten the strength and increase the ductility of xcex2-type titanium alloy bar wire. But it is difficult to obtain a straightness (characteristic of being straight). For example, it is impossible to improve the straightness even if the fine xcex2-type titanium alloy wire would be let into a general levelling roller or a rotary leveller. Because xcex2-type titanium alloy wire has a low Young""s modulus, even if the mechanical working for straightening the xcex2-titanium alloy wire by plastic deforming using roller would be conducted, an effect of the mechanical working cannot be expected.
It is difficult to apply the prior method for producing xcex2-titanium alloy bar wire to the production of metallic wires which are needed to have the straightness, such as communication cable, probe card pin for inspection of conduction, metallic fishing line and the like.
First problem is to provide the method for producing xcex2-titanium alloy wire with a high strength and a good, straightness.
(2) Second Problem
In accordance with the prior method for producing xcex2-titanium alloy bar wire, it is possible to heighten the strength but a low elastic modulus cannot be obtained.
It is difficult to apply the prior method for producing xcex2-titanium alloy bar wire to the production of metallic wires which are needed to have the low Young""s modulus (ductility), such as tension member for communication cable, probe card pin for inspection of conduction, metallic fishing line and the like.
Second problem is to provide xcex2-titanium alloy wire and method for its production with a low Young""s modulus (ductility) and a high strength.
(3) Third Problem
In accordance with the prior method for producing titanium alloy wire, wire rods have been heated at a temperature of 400 to 650xc2x0 C. in the atmosphere to generate the oxidation film on the surface of wire rods and a cold wire-drawing has been conducted by making use of lubrication of this film. However, all reduction ratio of area of cold wire-drawing by this prior method is 70% at a maximum. Since the above oxide film is hard and brittle, the oxide film would be cracked owing to a high reduction ratio of area and lubrication action would be lowering. If the cracked boundary face enlarges, titanium alloy wire would be damaged and breaking of wire would be generated. Accordingly, it is necessary to eliminate the embrittled oxide film by pickling and conduct the second treatment for generating the oxide film and repeat cold wire-drawing before enlargement of crack in the oxide film. For the reason, the number of production processes increases and the production cost becomes larger. Especially, in case of xcex2-titanium alloy, xcex1-phase would be precipitated in xcex2-phase and xcex2-titanium would be hardened because of heating at a temperature of 400 to 650xc2x0 C. in the atmosphere. As a result, long heating extremely lowers cold wire-drawability and brings a deterioration of mechanical strength.
There are the means for downsizing, such as roller die or swaging. But it is impossible to obtain a good circularity and an accuracy of dimension by those means. Accordingly, those would be in need of cold wire-drawing at sequential process.
For solving the above defects, it is disclosed in Patent Unexamined Publication No. 4-279212 that titanium wire is coated with copper and the repetition of cold wire-drawing and annealing are conducted to get thin titanium wire.
But, in accordance with the above art, since Young""s modulus of copper is higher than xcex2-titanium alloy, Young""s modulus totally gets higher.
It is difficult to apply this art to the production of metallic wires which are needed to have the high ductility, such as various kinds of precision springs, various kinds of ropes or cables, tension member, metallic fishing line and the like.
Third problem is to provide the method for producing xcex2-titanium alloy wire with a good lubricity and a good wire-drawability and a low wire-drawing cost and a high ductility.
(4) Fourth Problem
In consideration of the above defects on medical treatments, the fourth problem is to provide the guide wire for medical treatment and the catheter with moderate rigidity and ductility. The another problem is to provide the stent having a ductility for passing through the blood vessel and a moderate rigidity after placement to suppress re-stenosis.
For solving the first problem, the present invention is characterized in that wire-drawing of xcex2-titanium alloy is followed by two stages aging processes. By the first aging process, fine xcex1-phase is precipitated in xcex2-phase to heighten the strength. In the second aging process, since heat treatment is conducted under a supply of moderate tension, strain accompanied by wire-drawing is eliminated to improve the straightness.
For solving the second problem, the present invention is characterized by specifying the shape and the size of the xcex2-phase crystal. By this invention, it is possible to obtain xcex2-titanium alloy wire with a high strength and a low Young""s modulus.
For solving the third problem, the present invention is characterized in that center core of xcex2-titanium alloy is coated with the specified material to get a composite wire. By this invention, it is possible to conduct a cold wire drawing maintaining a good lubricity and a good drawability.
For solving the fourth problem, the present invention is characterized. by employing xcex2-titanium alloy wire comprising xcex2-phase crystal grain of the specified shape and size. By this invention, it is possible to provide a guide wire for medical treatment, catheter and stent, each of which has a moderate rigidity and a ductility respectively.
For solving the first, second, third and fourth problems, the present invention has the following features.
(1) The Invention xe2x80x9cAxe2x80x9d of Method for Producing xcex2-titanium Alloy Wire for Solving the First Problem
The gist of the invention xe2x80x9cAxe2x80x9d is that a method for producing xcex2-titanium alloy wire comprising the steps of reducing the diameter of xcex2-titanium alloy wire by cold wire-drawing followed by heat treatment is characterized in that the heat treatment comprises the first aging process for precipitation strengthening and the second aging process for removing a processing strain, and xcex2-titanium alloy wire is heat-treated under a supply of tension at the second aging process.
In accordance with the present invention, fine xcex1-phase is plentifully precipitated in the xcex2-phase of xcex2-titanium alloy wire to heighten the strength in the first aging process and then xcex2-titanium alloy wire is heat-treated under a supply of moderate tension to remove a strain accompanied by wire-drawing and improve the straightness in the second aging process. In this case, if a solid solution treatment is conducted at a temperature over xcex2-transformation point before cold wire-drawing and the structure is free from xcex1-phase, the cold workability would be improved to facilitate cold wire-drawing and evenly form a deformation texture of xcex2-phase.
xcex2-titanium is good in workability but easy to adhere to the others. It is preferable to coat xcex2-titanium wire with a moderate oxide film before the wire-drawing to avoid the adhesion to the surface of die at the wire-drawing.
Wire-drawing may be conducted by means of cassette roller die or holey die.
The temperature of 425 to 650xc2x0 C. is desirable for the first aging process. The reason is that if the temperature is over 650xc2x0 C., over-aging would be improperly done to lower the strength and if the temperature is under 425xc2x0 C., fine xcex1-phase could not be precipitated in spite of long time aging treatment. The processing time of the first aging process may be fitly set according to the diameter of wire. For example, if the diameter of wire is 10 xcexcm, the time of one minute to several minutes would be satisfactory for the first aging process and if the diameter of wire is 1 mm, the time for the first aging process may be set in the range of 4 to 48 hours. If the processing time is too short, fine xcex1-phase could not be precipitated in plenty. If the processing time is too long, the quantity of precipitated xcex1-phase does not increase so much.
If the temperature of the second aging process is under 300xc2x0 C., the processing strain could not be removed and the straightness could not be improved even under the supply of tension. If the temperature of the second aging process is over 600xc2x0 C., the change of metal structure such as solution would be improperly generated to lower the ductility. For this reason, the temperature of 300 to 600xc2x0 C. is desirable for the second aging process.
If the processing time of the second aging process is too short, the processing strain could not be removed and the straightness could not be improved under the supply of tension. If the processing time is too long, the effect would be not only unchanged but also the prodution efficiency would be lowered. For this reason, the time of 3 to 10 minutes is desirable for the second aging process.
The strength of 0.1 to 30% of breaking load of xcex2-titanium alloy wire is desirable for the tension to be supplied to xcex2-titanium alloy wire at the second aging process. If the strength is under 0.1% of said breaking load, the degree of improvement fo straightness would be small. If the strength is over 30% of said breaking load, there is a possibility that titanium wire would extend. Furthermore, the strength of 0.5 to 10% of breaking load of xcex2-titanium alloy wire is more desirable for the tension to be supplied to xcex2-titanium alloy wire at the second aging process. There are many machinery structual restrictions and no ecomical merit as actual industrial equipment in case of controlling tension in the range of less than 0.5% of said breaking load. In consideration of the variation in rewinding tension of titanium wire, since it is feared that an instant maximum tension, would become much larger than. a setting tension, the setting tension of less than 10% of the breaking load is realistic.
Most of the diameter of metallic wires, such as tension member for communication cable, probe card pin for inspection of conduction, metallic fishing line and the like are in the range of 0.01 to 2.0 mm. xcex2-titanium alloy wire of diameter of 0.01 to 2.0 mm is suitable for metallic wire of these applications. Especially, since the required level (as described later) of the straightness of the probe card pin is, extremely severe and lower than 0.3 to 50 mm, xcex2-titanium alloy wire of the present invention, which is good in straightness, is suitable for this application.
(2) The Invention xe2x80x9cBxe2x80x9d of xcex2-titanium Alloy Wire and Method for its Production for Solving the Second Problem
The gist of the invention xe2x80x9cBxe2x80x9d is xcex2-titanium alloy wire comprises a diameter of 0.01 to 2.0 mm, an average crystal grain area A of xcex2-phase in cross section structure is 1 to 80 xcexcm2, an average crystal grain length L of xcex2-phase in vertical section structure is 10 to 1000 xcexcm and a ratio of L/{square root over ( )}A is 5 to 1000.
The reasons for restricting the factors specifying the shape and the size are as follows:
If the diameter of xcex2-titanium alloy wire is less than 0.01 mm, it is not possible to obtain a practical strength. If the diameter of xcex2-titanium alloy wire is more than 2.0 mm, the wire would have a low Young""s modulus but no ductility could not be obtained.
It is very difficult and not realistic to obtain xcex2-titanium alloy wire, whose average crystal grain area A of xcex2-phase in cross section structure is under 1 xcexcm2, by wire-drawing. xcex2-titanium alloy, whose average crystal grain area A of xcex2-phase in cross section structure is over 80 xcexcm2, shows a low strength and is not desirable for solving the the present invention""s problem.
It reveals a defect of being insufficient in strength that an average crystal grain length L of xcex2-phase in vertical section structure is under 10 xcexcm. It is difficult to obtain xcex2-titanium alloy wire, whose average crystal grain length L of xcex2-phase in vertical section structure is over 1000 xcexcm, by machining.
As for a relation between an average crystal grain length L and an average crystal grain area A, if L/{square root over ( )}A is under 5, it is impossible to obtain a sufficient strength and ductility, and then it is difficult to machine xcex2-titanium alloy wire so that L/{square root over ( )}A would be over 1000.
As described above, by restricting a diameter of wire, an average crystal grain area A of xcex2-phase in cross section structure, an average crystal grain length L of xcex2-phase in vertical section structure and a ratio of L/{square root over ( )}A to the specified ranges of the present invention, xcex2-titanium alloy wire with a high strength and a low Young""s modulus can be obtained.
For producing xcex2-titanium alloy wire of the present invention, It is preferable that xcex2-titanium alloy would be subjected to solid solution treatment at a temperature of more than xcex2-transformation point to get a structure free from xcex2-phase before cold wire-drawing. As a result, cold workability is improved to facilitate cold wire-drawing and evenly form a deformation texture of xcex2-phase.
xcex2-titanium is good in workability but easy to adhere to the others. It is preferable to coat xcex2-titanium alloy wire with a moderate oxide film before wire-drawing to avoid the adhesion to the surface of die at the wire-drawing.
Wire-drawing may be conducted by means of cassette roller die or holey die.
It is possible to precipitate fine xcex1-phase in xcex2-phase and heighten the strength by a moderate aging treatment after wire-drawing. It is preferable that the aging temperature would be in the range of 400 to 600xc2x0 C. and the aging time would be in the raneg of 1 to 24 hours.
For obtaining xcex2-titanium alloy wire comprising the above dintinctive crystal grain shape, it is necessay that all reduction ratio of area by cold wire-drawing would stand at 70% or more. All reduction ratio of area of 90% or more is desirable for the present invention but all reduction ratio of area of more than 99% would generate a work hardening leading to embrittlement.
Most of the diameter of metallic wires, such as tension member for communication cable, probe card pin for inspection of conduction, metallic fishing line and the like are in the range of 0.01 to 2.0 mm. xcex2-titanium alloy wire of diameter of 0.01 to 2.0 mm to be produced by the method of the present invention is suitable for metallic wire of these applications.
(3) The Invention xe2x80x9cCxe2x80x9d of Method for Producing xcex2-titanium Alloy Wire for Solving the Third Problem
The gist of the invention xe2x80x9cCxe2x80x9d is characterized in that that a center core of xcex2-titanium alloy is coated with the outer shroud comprising aluminum or aluminum alloy to get a integrated composite wire and then gives the cold wire-drawing to said composite wire.
In accordance with the present invention, since the center core of xcex2-titanium alloy is coated with aluminum or aluminum alloy, xcex2-titanium alloy would not be oxidized and titanium oxide which degrade wire-drawability would not be formed. Since coating of aluminum or aluminum alloy has a good ductility, xcex2-titanium alloy with this coating is little hardened even though cold wire-drawing of high reduction ratio of area would be conducted. Thus, a good wire-drawability and lubricity would be maintained. As a result, it is possible to make cold wire-drawing of all reduction ratio of area of more than 90%. Furthermore, since xcex2-titanium as well as aluminum has a low Young""s modulus, young modulus of a integrated compound wire becomes low, too. Therefore, xcex2-titanium alloy wire of good ductility can be obtained.
A stable and sure cold wire-drawing becomes possible through means that a ratio of cross section area of the outer shroud to all cross section area of composite wire before cold wire-drawing is 20 to 60%. If said ratio of cross section area of the outer shroud is under 20%, titanium alloy of center core would be partially exposed at cold wire-drawing, with the result that cold wire-drawability would be lowered. If said ratio of cross section area of the outer shroud is over 60%, the strength per unit cross section area of composit wire would extremely lower, with the result that this composite wire would not be suitable for various kinds of precision springs, various kinds of ropes or cables, tension member, metallic fishing line and the like.
It is more preferable that the above ratio of cross section area of the outer shroud would be 30 to 50%.
For coating the center core of xcex2-titanium alloy with the outer shroud comprising aluminum or aluminum alloy, it is preferable that xcex2-titanium wire passes through aluminum pipe or aluminum alloy pipe and then the center core is adhered closely to the outer shroud by swaging or roller die machining. The composite wire obtained by this manner is repeatedly made cold wire-drawing or heat treatment and the wire comprising the requested size can be obtained.
(4) The Inventions of Guide Wire for Medical Treatment, Catheter and Stent for Solving the Fourth Problem
The gist of the invention of guide wire for medical treatment is characterized by employing xcex2-titanium alloy wire that an average crystal grain area A of xcex2-phase in cross section structure is 1 to 80 xcexcm2, an average crystal grain length L of xcex2-phase in vertical section structure is 10 to 1000 xcexcm and a ratio of L/{square root over ( )}A is 5 to 1000.
The gist of the invention of catheter is characterized by employing xcex2-titanium alloy wire that an average crystal grain area A of xcex2-phase in cross section structure is 1 to 80 xcexcm2, an average crystal grain length L of xcex2-phase in vertical section structure is 10 to 1000 xcexcm and a ratio of L/{square root over ( )}A is 5 to 1000.
The gist of the invention of stent is characterized by employing xcex2-titanium alloy wire that an average crystal grain area A of xcex2-phase in cross section structure is 1 to 80 xcexcm2, an average crystal grain length L of xcex2-phase in vertical section structure is 10 to 1000 xcexcm and a ratio of L/{square root over ( )}A is 5 to 1000.